def test_Dict():
assert str(Dict({1: 1 + x})) == sstr({1: 1 + x}) == "{1: x + 1}"
assert str(Dict({
1: x**2,
2: y * x
})) in ("{1: x**2, 2: x*y}", "{2: x*y, 1: x**2}")
assert sstr(Dict({1: x**2, 2: y * x})) == "{1: x**2, 2: x*y}"
def test_Dict():
assert str(Dict({1: 1 + x})) == sstr({1: 1 + x}) == '{1: x + 1}'
assert str(Dict({
1: x**2,
2: y * x
})) in ('{1: x**2, 2: x*y}', '{2: x*y, 1: x**2}')
assert sstr(Dict({1: x**2, 2: y * x})) == '{1: x**2, 2: x*y}'
def test_domains():
X, Y = Die('x', 6), Die('y', 6)
x, y = X.symbol, Y.symbol
# Domains
d = where(X > Y)
assert d.condition == (x > y)
d = where(And(X > Y, Y > 3))
assert d.as_boolean() == Or(And(Eq(x, 5), Eq(y,
4)), And(Eq(x, 6), Eq(y, 5)),
And(Eq(x, 6), Eq(y, 4)))
assert len(d.elements) == 3
assert len(pspace(X + Y).domain.elements) == 36
Z = Die('x', 4)
pytest.raises(ValueError,
lambda: P(X > Z)) # Two domains with same internal symbol
assert pspace(X + Y).domain.set == FiniteSet(1, 2, 3, 4, 5, 6)**2
assert where(X > 3).set == FiniteSet(4, 5, 6)
assert X.pspace.domain.dict == FiniteSet(
*[Dict({X.symbol: i}) for i in range(1, 7)])
assert where(X > Y).dict == FiniteSet(*[
Dict({
X.symbol: i,
Y.symbol: j
}) for i in range(1, 7) for j in range(1, 7) if i > j
])
def test_gcd_terms():
f = 2*(x + 1)*(x + 4)/(5*x**2 + 5) + (2*x + 2)*(x + 5)/(x**2 + 1)/5 + \
(2*x + 2)*(x + 6)/(5*x**2 + 5)
assert _gcd_terms(f) == (Rational(6, 5) * ((1 + x) / (1 + x**2)), 5 + x, 1)
assert _gcd_terms(Add.make_args(f)) == \
(Rational(6, 5)*((1 + x)/(1 + x**2)), 5 + x, 1)
newf = Rational(6, 5) * ((1 + x) * (5 + x) / (1 + x**2))
assert gcd_terms(f) == newf
args = Add.make_args(f)
# non-Basic sequences of terms treated as terms of Add
assert gcd_terms(list(args)) == newf
assert gcd_terms(tuple(args)) == newf
assert gcd_terms(set(args)) == newf
# but a Basic sequence is treated as a container
assert gcd_terms(Tuple(*args)) != newf
assert gcd_terms(Basic(Tuple(1, 3*y + 3*x*y), Tuple(1, 3))) == \
Basic((1, 3*y*(x + 1)), (1, 3))
# but we shouldn't change keys of a dictionary or some may be lost
assert gcd_terms(Dict((x*(1 + y), 2), (x + x*y, y + x*y))) == \
Dict({x*(y + 1): 2, x + x*y: y*(1 + x)})
assert gcd_terms((2 * x + 2)**3 +
(2 * x + 2)**2) == 4 * (x + 1)**2 * (2 * x + 3)
assert gcd_terms(0) == 0
assert gcd_terms(1) == 1
assert gcd_terms(x) == x
assert gcd_terms(2 + 2 * x) == Mul(2, 1 + x, evaluate=False)
arg = x * (2 * x + 4 * y)
garg = 2 * x * (x + 2 * y)
assert gcd_terms(arg) == garg
assert gcd_terms(sin(arg)) == sin(garg)
# issue sympy/sympy#6139-like
alpha, alpha1, alpha2, alpha3 = symbols('alpha:4')
a = alpha**2 - alpha * x**2 + alpha + x**3 - x * (alpha + 1)
rep = {
alpha: (1 + sqrt(5)) / 2 + alpha1 * x + alpha2 * x**2 + alpha3 * x**3
}
s = (a / (x - alpha)).subs(rep).series(x, 0, 1)
assert simplify(collect(s, x)) == -sqrt(5) / 2 - Rational(3, 2) + O(x)
# issue sympy/sympy#5917
assert _gcd_terms([Integer(0), Integer(0)]) == (0, 0, 1)
assert _gcd_terms([2 * x + 4]) == (2, x + 2, 1)
eq = x / (x + 1 / x)
assert gcd_terms(eq, fraction=False) == eq
def test_IndexedBase_subs():
i = Symbol('i', integer=True)
A = IndexedBase(a)
B = IndexedBase(b)
C = IndexedBase(c)
assert A[i] == B[i].subs({b: a})
assert isinstance(C[1].subs({C: Dict({1: 2})}), type(A[1]))
def test_ndim_array_initiation():
arr_with_one_element = ImmutableDenseNDimArray([23])
assert len(arr_with_one_element) == 1
assert arr_with_one_element[0] == 23
assert arr_with_one_element[:] == [23]
assert arr_with_one_element.rank() == 1
arr_with_symbol_element = ImmutableDenseNDimArray([Symbol('x')])
assert len(arr_with_symbol_element) == 1
assert arr_with_symbol_element[0] == Symbol('x')
assert arr_with_symbol_element[:] == [Symbol('x')]
assert arr_with_symbol_element.rank() == 1
number5 = 5
vector = ImmutableDenseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5, )
assert vector.rank() == 1
vector = ImmutableSparseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5, )
assert vector._sparse_array == Dict()
assert vector.rank() == 1
n_dim_array = ImmutableDenseNDimArray(range(3**4), (
3,
3,
3,
3,
))
assert len(n_dim_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == (3, 3, 3, 3)
assert n_dim_array.rank() == 4
array_shape = (3, 3, 3, 3)
sparse_array = ImmutableSparseNDimArray.zeros(*array_shape)
assert len(sparse_array._sparse_array) == 0
assert len(sparse_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == array_shape
assert n_dim_array.rank() == 4
one_dim_array = ImmutableDenseNDimArray([2, 3, 1])
assert len(one_dim_array) == 3
assert one_dim_array.shape == (3, )
assert one_dim_array.rank() == 1
assert one_dim_array.tolist() == [2, 3, 1]
shape = (3, 3)
array_with_many_args = ImmutableSparseNDimArray.zeros(*shape)
assert len(array_with_many_args) == 3 * 3
assert array_with_many_args.shape == shape
assert array_with_many_args[0, 0] == 0
assert array_with_many_args.rank() == 2
def test_Dict():
x, y, z = symbols('x y z')
d = Dict({x: 1, y: 2, z: 3})
assert d[x] == 1
assert d[y] == 2
pytest.raises(KeyError, lambda: d[2])
assert len(d) == 3
assert set(d.keys()) == {x, y, z}
assert set(d.values()) == {Integer(1), Integer(2), Integer(3)}
assert d.get(5, 'default') == 'default'
assert x in d and z in d and 5 not in d
assert d.has(x) and d.has(1) # Diofant Basic .has method
# Test input types
# input - a python dict
# input - items as args - Diofant style
assert (Dict({x: 1, y: 2, z: 3}) == Dict((x, 1), (y, 2), (z, 3)))
pytest.raises(TypeError, lambda: Dict(((x, 1), (y, 2), (z, 3))))
with pytest.raises(NotImplementedError):
d[5] = 6 # assert immutability
assert set(d.items()) == {
Tuple(x, Integer(1)),
Tuple(y, Integer(2)),
Tuple(z, Integer(3))
}
assert set(d) == {x, y, z}
assert str(d) == '{x: 1, y: 2, z: 3}'
assert d.__repr__(
) == "Dict(Tuple(Symbol('x'), Integer(1)), Tuple(Symbol('y'), Integer(2)), Tuple(Symbol('z'), Integer(3)))"
# Test creating a Dict from a Dict.
d = Dict({x: 1, y: 2, z: 3})
assert d == Dict(d)
def __new__(cls, *args, **kwargs):
shape, flat_list = cls._handle_ndarray_creation_inputs(*args, **kwargs)
shape = Tuple(*map(_sympify, shape))
loop_size = functools.reduce(lambda x, y: x * y, shape) if shape else 0
# Sparse array:
if isinstance(flat_list, (dict, Dict)):
sparse_array = Dict(flat_list)
else:
sparse_array = {}
for i, el in enumerate(flatten(flat_list)):
if el != 0:
sparse_array[i] = _sympify(el)
sparse_array = Dict(sparse_array)
self = Expr.__new__(cls, sparse_array, shape, **kwargs)
self._shape = shape
self._rank = len(shape)
self._loop_size = loop_size
self._sparse_array = sparse_array
return self
def test_dict_set():
a, b = map(Wild, 'ab')
f = 3 * cos(4 * x)
r = f.match(a * cos(b * x))
assert r == {a: 3, b: 4}
e = a / b * sin(b * x)
assert e.subs(r) == r[a] / r[b] * sin(r[b] * x)
assert e.subs(r) == 3 * sin(4 * x) / 4
s = set(r.items())
assert e.subs(s) == r[a] / r[b] * sin(r[b] * x)
assert e.subs(s) == 3 * sin(4 * x) / 4
assert e.subs(r) == r[a] / r[b] * sin(r[b] * x)
assert e.subs(r) == 3 * sin(4 * x) / 4
assert x.subs(Dict((x, 1))) == 1
def test_ProductPSpace():
X = Normal('X', 0, 1)
Y = Normal('Y', 0, 1)
px = X.pspace
py = Y.pspace
assert pspace(X + Y) == ProductPSpace(px, py)
assert pspace(X + Y) == ProductPSpace(py, px)
X = Die('X', 2)
Y = Die('Y', 2)
assert (pspace(X + Y).density ==
Dict((frozenset({('X', 1), ('Y', 2)}), Rational(1, 4)),
(frozenset({('X', 1), ('Y', 1)}), Rational(1, 4)),
(frozenset({('X', 2), ('Y', 1)}), Rational(1, 4)),
(frozenset({('X', 2), ('Y', 2)}), Rational(1, 4))))
d = pspace(X + Y).domain
assert ((X.symbol, 1), (Y.symbol, 2)) in d
assert ((X.symbol, 0), (Y.symbol, 2)) not in d
Z = Die('Z', 2)
d1 = pspace(X + Y).domain
assert ProductDomain(d1, Z.pspace.domain) == pspace(X + Y + Z).domain
def __new__(cls, density):
density = Dict(density)
return Basic.__new__(cls, density)